Out the following steps in the proper sequence for simplifying a Boolean…

2024

Out the following steps in the proper sequence for simplifying a Boolean function using a Karnaugh map (K-map). (A) Identify and group the largest possible cluster of 1's (B) Draw the K-map for the given Boolean function (C) Write the simplified Boolean expression from the grouped clusters (D) Transfer the truth table values to the K-map
Choose the correct answer from the options given below:

Answer: A. (B), (D), (A), (C)Correct sequence: Draw the Karnaugh map for the given Boolean function (set up the correct number of variables, cell order, and labels). Transfer the truth…

  1. A.

    (B), (D), (A), (C)

  2. B.

    (D), (B), (A), (C)

  3. C.

    (B), (A), (D), (C)

  4. D.

    (A), (B), (C), (D)

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Show answer & explanation

Correct answer: A

Correct sequence:

  1. Draw the Karnaugh map for the given Boolean function (set up the correct number of variables, cell order, and labels).

  2. Transfer the truth table values to the K-map (fill each cell with the function value from the truth table).

  3. Identify and group the largest possible clusters of 1s (groups must be powers of two: 1, 2, 4, 8, ...; groups may overlap and wrap around map edges).

  4. Write the simplified Boolean expression from the grouped clusters (derive a product or sum term for each group, then combine).

Why this order?

You need the map layout before placing values so each truth-table entry maps to the correct cell. Grouping depends on the placed values, and simplification follows directly from those groups.

Quick tips:

  • Always form the largest possible groups (they yield the simplest terms).

  • Groups can overlap if that helps make them larger and reduce terms.

  • Remember wrap-around adjacency: opposite edges are adjacent in a K-map.

  • Check for redundant groups and remove them when they do not change the simplified expression.

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